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This paper proposes a simple, closed-form switch ing formula for determining the optimal gait transition speeds of legged robots. For robots with even-numbered legs that are arranged symmetrically along the direction of locomotion, the formula determines the forward locomotion speed at which running (gallop) becomes more efficient than walking (trot).The accuracy of the switching formula is empirically evalu ated through a series of dynamic optimization procedures for bipeds and quadrupeds: in each case, after determining the most energy-efficient walking and running gaits for a given desired speed, the common intersection of the speed-energy efficiency graphs for the two gaits is then taken to be the gait transition point. Our switching formula is then applied to various animals(human, ostrich, horse, dog and elephant), where the gait transition speeds predicted by our formula are found to be remarkably close to the actual transition speeds of the animals.

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